represent in the following in the form of quadratic equations and solve it also.
a) the product of two-consecutive integer is 306
b)the length of the rectangular park is one of the more than twice it's breadth and it's area is 528m^2
Answers
Correct question :
Represent the following situations in the form of quadratic equations:
(a) The product of two consecutive positive integers is 306. We need to find the integers.
(b) The area of a rectangular plot is 528 m². The length of the plot (inmetres) is one more than twice its breadth. We need to find the length and breadth of the plot
Solution :
(a) Let the first integer be = x
Next consecutive positive integer = x + 1
According to question,
x (x + 1) = 306
x² + x = 306
x² + x - 306 = 0 ............ (1)
∴ This is the form of quadratic equation where x is the smallest positive integer..
(b) Let the breadth of the rectangular plot = x m
Length of the plot (2x +1) m
Area of rectangle = length x breadth 528 m²
According to question,
(2x+1) x x = 528
2x² + x = 528
2x² + x - 528 = 0 .............. (1)
∴ This is the form of quadratic equation where the breadth is in metres.